WASHINGTON (CNN) -- Some coastal cities and liberal strongholds that have declared themselves safe places for undocumented immigrants -- "sanctuary cities" -- have been bracing for the fallout from the new Trump administration.

Chicago Mayor Rahm Emanuel, President Barack Obama's former chief of staff, said Monday at a news conference that city officials have been fielding calls from residents worried that it may change its status because of the threat from Trump.

"Since the presidential election, there has been a sense of uncertainty among many immigrant communities in Chicago and across the nation," Emanuel said. "I want to assure all of our families that Chicago is and will remain a sanctuary city."

The sanctuary city designation broadly means that local police will not coordinate with federal law enforcement in efforts to deport undocumented immigrants.

Trump promised on the campaign trail that he would block federal funding for sanctuary cities.

"Block funding for sanctuary cities. We block the funding. No more funds," Trump said in August, in his much-touted immigration speech. "We will end the sanctuary cities that have resulted in so many needless deaths. Cities that refuse to cooperate with federal authorities will not receive taxpayer dollars, and we will work with Congress to pass legislation to protect those jurisdictions that do assist federal authorities."

He has not said since then if he would follow through on the promise, and whether it would need congressional approval or could be done through executive order.

The Trump transition team did not immediately respond to CNN requests for comment Monday.

But there are signs indicating he is likely to stick to a hard-line immigration stance.

Trump tapped Steve Bannon, a Breitbart news publisher who has embraced the white nationalist and alt-right movements, to be his chief strategist, placing him on an equal footing with incoming chief of staff Reince Priebus. Immigration and sanctuary cities in particular have been a hot-button issue for conservatives, stoked in part by coverage from the Bannon-led Breitbart.com.

That has left city officials across the country planning for the worst if they lose all their federal aid.

Officials in San Francisco said they receive up to $1 billion in federal aid.

"It's certainly something the mayor's office, the city's lobbyist and our office has started looking at," City Controller Ben Rosenfield, told The San Francisco Chronicle last week.

And Crain's New York Business determined that Trump's home city, New York, could take a $6 billion hit if he follows through with the plans.

"These are our fellow New Yorkers, we're going to respect them, protect them, they're part of our communities," New York Mayor Bill de Blasio, a supporter of Hillary Clinton, told the paper.